It certainly does not CAUSE acne, but it can aggravate it. I have severe acne and when I don't ejaculate for a couple of days my skin actually gets better. The reason is simply because Testosterone doesn't get turned into Dihydrotestosterone when you don't fap. DHT is responsible for acne, hair loss etc.
Acne can't be cured by just doing NoFap. Eventually, you'll have to fap anyways and you'll break out again. Go see a dermatologist if you have mediocre-severe acne. I've been on accutane for almost two months now and my skin already doesn't get oily anymore, which means that the acne bacterium is not able to grow as easily. I get around 3 new pimples every day at the moment. When I do NoFap it's like 1.